Abstract

We describe a model-based instrument design combined with a statistical classification approach for the development and realization of high speed cell classification systems based on light scatter. In our work, angular light scatter from cells of four bacterial species of interest, Bacillus subtilis,Escherichia coli,Listeria innocua, and Enterococcus faecalis, was modeled using the discrete dipole approximation. We then optimized a scattering detector array design subject to some hardware constraints, configured the instrument, and gathered experimental data from the relevant bacterial cells. Using these models and experiments, it is shown that optimization using a nominal bacteria model (i.e., using a representative size and refractive index) is insufficient for classification of most bacteria in realistic applications. Hence the computational predictions were constituted in the form of scattering-data-vector distributions that accounted for expected variability in the physical properties between individual bacteria within the four species. After the detectors were optimized using the numerical results, they were used to measure scatter from both the known control samples and unknown bacterial cells. A multivariate statistical method based on a support vector machine (SVM) was used to classify the bacteria species based on light scatter signatures. In our final instrument, we realized correct classification of B. subtilis in the presence of E. coli,L. innocua, and E. faecalis using SVM at 99.1%, 99.6%, and 98.5%, respectively, in the optimal detector array configuration. For comparison, the corresponding values for another set of angles were only 69.9%, 71.7%, and 70.2% using SVM, and more importantly, this improved performance is consistent with classification predictions.

Figures (6)

(Color online) Forward scattering signatures for representative bacteria of the four species of interest, plotted as average differential scattering cross section (dCsc∕dω averaged over φ) versus forward scattering angle θ. The vertical lines indicate the center angles for the four ring apertures in the detector array. The two sets of four lines correspond to the two different measurement configurations, A (diamond ends) and B (circular ends).

(Color online) Variation of distinguishability with forward angle θ (averaged over all azimuth angles f) for representative bacteria of the four species. The two sets of four vertical lines correspond to the two different measurement configurations, A (diamond ends) and B (circular ends).

(Color online) Predicted scatter plots of ring-averaged forward scattering intensities (average dCsc/dω
over f) for detector configuration A for four bacterial species (note: size of subgroups are not to scale). Each data point represents the predicted signal pair for bacteria from a population distribution governed by Eq. (2) with the following:refractive index mean of 1.394 and standard deviation of 2%
and a normal volume distribution with standard deviation of 5%.

(Color online) Predicted scatter plots of ring-averaged forward scattering intensities (average dCsc/dω
over f) for detector configuration B for four bacterial species (note: sizes of subgroups are not to scale). Each data point represents the predicted signal pair for bacteria from a population distribution governed by Eq. (2) with the following:refractive index mean of 1.394 and standard deviation of 2%
and a normal volume distribution with standard deviation of 5%.

Table 1

Performance Predictions for Advanced Cytometers based on Multiangle Scatter Detector Configurations A and Ba

Classification Rates Predicted Using Full Model with Bacteria Population Distributions from Eq. (2)c

A

B

A

B

E. faecalis versus B. subtilis

2.25

2.01

100%

87%

E. faecalis versus L. innocua

2.42

3.12

95%

79%

E. faecalis versus E. coli

1.34

0.67

77%

61%

E. coli versus B. subtilis

2.15

1.49

100%

81%

E. coli versus L. innocua

1.88

2.82

95%

79%

B. subtilis versus L. innocua

2.11

1.79

98%

74%

a Two cases where the simple distinguishability predictions and the classification rate predicted by the full simulation differ in trend are in bold.b Assuming a single representative bacteria size and effective refractive index.cno = 1.394, σn = 2%, σv = 5% (rounded to nearest integer %).

Table 2

Classification Rates of Bacteria for Multiangle Light Scatter Detector Configurations A and B

Bacteria Species Pairs

Predicted Classification Rates based on Full Model with Bacteria Population Distributions from Eq. (2)a

Tables (2)

Table 1

Classification Rates Predicted Using Full Model with Bacteria Population Distributions from Eq. (2)c

A

B

A

B

E. faecalis versus B. subtilis

2.25

2.01

100%

87%

E. faecalis versus L. innocua

2.42

3.12

95%

79%

E. faecalis versus E. coli

1.34

0.67

77%

61%

E. coli versus B. subtilis

2.15

1.49

100%

81%

E. coli versus L. innocua

1.88

2.82

95%

79%

B. subtilis versus L. innocua

2.11

1.79

98%

74%

a Two cases where the simple distinguishability predictions and the classification rate predicted by the full simulation differ in trend are in bold.b Assuming a single representative bacteria size and effective refractive index.cno = 1.394, σn = 2%, σv = 5% (rounded to nearest integer %).

Table 2

Classification Rates of Bacteria for Multiangle Light Scatter Detector Configurations A and B

Bacteria Species Pairs

Predicted Classification Rates based on Full Model with Bacteria Population Distributions from Eq. (2)a